"The bear is writing a long love letter to the girl, because it thinks she is so beautiful."
Translation:Bjørnen skriver et langt kærlighedsbrev til pigen, fordi den synes hun er så smuk.
Yes, as far as I understand, the usage of at with synes is optional; it can be ommitted. But it should be correct when it is not ommited. So it should be accepted.
I have checked many sentences given by Duolingo, here are two of them: One with at and the other without at, when the synes structure is before a whole sentence:
Does anyone know for sure?
Well, I've been taught by DUO that the continuous aspect in Danish could be expressed with the help of such word combinations as "staar og skriver", "sidder og skriver" or " er ved at skriver", etc. Then what is wrong with "Bjoernen sidder og skriver et langt kaerlighedsbrev til....."?